Ground state solutions for quasilinear Schrodinger systems

This paper is concerned with the quasilinear Schrodinger systems in R-N: { -Delta u + (lambda a(x) + 1)u - 1/2 (Delta|u|(2)) u = 2 alpha/alpha+beta|u|(alpha-2) |nu|(beta) u, -Delta v + (lambda b(x) + 1)v - 1/2 (Delta|v|(2)) v = 2 beta/alpha+beta|u|(alpha) |nu|(beta-2) v, u(x) -> 0, v(x) -> 0 as |x| -> infinity, where lambda > 0 is a parameter, alpha > 2, beta >2, alpha + beta < 2.2* and 2* = 2N/2-2 for N >= 3, 2* = +infinity for N = 1, 2 is the critical Sobolev exponent. By using the Nehari manifold method and concentration compactness principle in the Orlicz space, we prove the existence of ground state solution which localize near the potential well int{a(-1) (0)} = int b(-1) (0) for lambda large enough. (C) 2011 Elsevier Inc. All rights reserved.